Fourier transformation is a mathematical operation with many applications, ranging from communication signal processing, differential equation analysis, image processing, audio processing, spectroscopy processing and so forth. For purposes of performing the Fourier transform in a digital processing system, the Fourier transform may be performed using a discrete transform, such as a Discrete Fourier Transform. The Discrete Fourier Transform is a matrix operation in which a real or complex value input vector (a vector representing sampled values for a temporally or spatially varying input signal, for example) is transformed into a complex value output vector (a vector representing frequency and phase components of the input signal, for example).
Convolution is a mathematical operation on two functions that produces a third function that is typically viewed as a modified version of one of the original functions. Convolution has applications that include image processing, probability, statistics, computer signal processing, electrical engineering, and differential equations. For large scale input signals and kernels, fast convolution operations may be computed in the frequency domain using a Discrete Fourier Transformation.
A resistive memory array can be utilized to perform analog computations that exploit the fundamental relationship between row voltage and column current in a resistive mesh to realize an analog multiply-accumulate unit. Such a unit may be faster than a digital computation, and may also consume significantly lower energy than traditional digital functional units. The memory array is typically organized as a grid of cells interconnected by horizontal and vertical wires, referred to as word/row lines and bit/column lines. The fundamental relationship between a row access voltage and a resulting bit line current can act as an analog multiplier of row voltage and memory array cell conductance. Large crossbar arrays of memory devices with memristors can be used in a variety of applications, including memory, programmable logic, signal processing control systems, pattern recognition, and other applications.